To get True boton Flava you should go to Boston Beer Works - Right across from Fenway. The north end is pretty far from Fenway - Opposite ends of the city - You c hop on the T if its not nice out, if its a nice day you can walk.
You can always go to Newbury street they have lots of resturants - some are not too expensive. Charlies ( i think - has a great outdoor patio and Stephanies - a little more upscale). If you head out onto Boylston ( it runs parallel to Newbury) there are lots of places: Cactus Club, Whiskeys, Poor House...those are all inexpensive and fun. Let me know if you have any other questions - I am really familiar with the city.